To determine the how many number of years keep burning the bulb by mass defect energy of 1mole 14 C keep a 100-W light bulb burning. Concept introduction: Mass defect: The nucleus of each atom (aside from 1 1 H ) has a mass lower than expected from adding the masses of its neutrons and protons. Mass and energy are related by following equation. E = m c 2 E= Energy m= mass c = speed of light . Loss of mass and liberation of energy are related by Einstein’s equations. E = (Δm)c 2 Δm = Mass defect c = Velocity of light

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Answer 1

Question

Chapter 14, Problem 14.43PAE

Interpretation Introduction

Interpretation: To determine the how many number of years keep burning the bulb by mass defect energy of 1mole $14C$ keep a 100-W light bulb burning.

Concept introduction: Mass defect:

The nucleus of each atom (aside from $11H$ ) has a mass lower than expected from adding the masses of its neutrons and protons.

Mass and energy are related by following equation.

$E=mc2$

E= Energy

m= mass

c = speed of light.

Loss of mass and liberation of energy are related by Einstein’s equations.

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Expert Solution & Answer

Answer to Problem 14.43PAE

Solution:

The mass defect energy keeps the burning up to 3221years.

Explanation of Solution

Formula used:

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Calculation: Let’s calculate the calculated mass of $14C$

$14C$ have six protons and eight neutrons.

$14Ccal= mH+ mNMass of proton =1.007825 uMass of neutron =1.008665 u$

$=6(1.007825 u) + 8(1.008665 u)=6.04695 u + 8.06932 u=14.11627 u$

The calculated mass of $14C$ is 14.11627 u.

Let’s calculate the mass defect

$Δm = 14Ccal-14CobsCalculated mass of 14C =14.11627 uActual mass of 14C =14.003242 u$

$=14.11627 u -14.003242 u= 0.113028 u$

Mass defect of $14C$ is 0.113028 u.

Let’s find the binding energy

$1 J = 1 kg m2 s-2$

$E = (Δm)c2Δm = mass defect = 0.113028 u= 0.113028 u×( 1 .66054×10 -27 kgu) × (3× 10 8)2=1.68685 × 10-11 kg m2s-2=1.68685 × 10-11 J$

Let’s calculate the energy release when $14C$ nucleus forms from its constituent nucleon. For 1 mole of $14C$ nuclei.

$E =( 1 .68685×10 -11 J 1 atom)( 6 .02214×10 23 atoms 1 mol)= 10.15845×1012 J/mol= 10.15845×109 kJ/mol$

Energy released by 1 mole of $14C$ nuclei is $10.15845 × 109 kJ/mol$ .

If it takes 360kJ of energy to keeps a 100-watt light bulb burning for 1 hour.

Assuming light bulb won’t burn out.

Let’s calculate the how many years this energy of carbon -14 could keep bulb burning.

From the given, 360 kJ will burn for 1 hour.

$(10.15845 × 109 kJ) (1 hr360 kJ) = 2.821791× 107 hrs$

Let’s converts hours into days.

$1 day = 24 hrs1 year = 365 days$

$=(2.821791×107 hrs)( 1 day 24 hrs)( 1 year 365 days)=3221 years$

Therefore, the mass defect energy keeps the burning up to 3221 years.

Conclusion

Therefore, the mass defect energy keeps the burning up to 3221 years.

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Answer 2

Question

Chapter 14, Problem 14.43PAE

Interpretation Introduction

Interpretation: To determine the how many number of years keep burning the bulb by mass defect energy of 1mole $14C$ keep a 100-W light bulb burning.

Concept introduction: Mass defect:

The nucleus of each atom (aside from $11H$ ) has a mass lower than expected from adding the masses of its neutrons and protons.

Mass and energy are related by following equation.

$E=mc2$

E= Energy

m= mass

c = speed of light.

Loss of mass and liberation of energy are related by Einstein’s equations.

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Expert Solution & Answer

Answer to Problem 14.43PAE

Solution:

The mass defect energy keeps the burning up to 3221years.

Explanation of Solution

Formula used:

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Calculation: Let’s calculate the calculated mass of $14C$

$14C$ have six protons and eight neutrons.

$14Ccal= mH+ mNMass of proton =1.007825 uMass of neutron =1.008665 u$

$=6(1.007825 u) + 8(1.008665 u)=6.04695 u + 8.06932 u=14.11627 u$

The calculated mass of $14C$ is 14.11627 u.

Let’s calculate the mass defect

$Δm = 14Ccal-14CobsCalculated mass of 14C =14.11627 uActual mass of 14C =14.003242 u$

$=14.11627 u -14.003242 u= 0.113028 u$

Mass defect of $14C$ is 0.113028 u.

Let’s find the binding energy

$1 J = 1 kg m2 s-2$

$E = (Δm)c2Δm = mass defect = 0.113028 u= 0.113028 u×( 1 .66054×10 -27 kgu) × (3× 10 8)2=1.68685 × 10-11 kg m2s-2=1.68685 × 10-11 J$

Let’s calculate the energy release when $14C$ nucleus forms from its constituent nucleon. For 1 mole of $14C$ nuclei.

$E =( 1 .68685×10 -11 J 1 atom)( 6 .02214×10 23 atoms 1 mol)= 10.15845×1012 J/mol= 10.15845×109 kJ/mol$

Energy released by 1 mole of $14C$ nuclei is $10.15845 × 109 kJ/mol$ .

If it takes 360kJ of energy to keeps a 100-watt light bulb burning for 1 hour.

Assuming light bulb won’t burn out.

Let’s calculate the how many years this energy of carbon -14 could keep bulb burning.

From the given, 360 kJ will burn for 1 hour.

$(10.15845 × 109 kJ) (1 hr360 kJ) = 2.821791× 107 hrs$

Let’s converts hours into days.

$1 day = 24 hrs1 year = 365 days$

$=(2.821791×107 hrs)( 1 day 24 hrs)( 1 year 365 days)=3221 years$

Therefore, the mass defect energy keeps the burning up to 3221 years.

Conclusion

Therefore, the mass defect energy keeps the burning up to 3221 years.

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Answer 3

Question

Chapter 14, Problem 14.43PAE

Interpretation Introduction

Interpretation: To determine the how many number of years keep burning the bulb by mass defect energy of 1mole $14C$ keep a 100-W light bulb burning.

Concept introduction: Mass defect:

The nucleus of each atom (aside from $11H$ ) has a mass lower than expected from adding the masses of its neutrons and protons.

Mass and energy are related by following equation.

$E=mc2$

E= Energy

m= mass

c = speed of light.

Loss of mass and liberation of energy are related by Einstein’s equations.

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Expert Solution & Answer

Answer to Problem 14.43PAE

Solution:

The mass defect energy keeps the burning up to 3221years.

Explanation of Solution

Formula used:

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Calculation: Let’s calculate the calculated mass of $14C$

$14C$ have six protons and eight neutrons.

$14Ccal= mH+ mNMass of proton =1.007825 uMass of neutron =1.008665 u$

$=6(1.007825 u) + 8(1.008665 u)=6.04695 u + 8.06932 u=14.11627 u$

The calculated mass of $14C$ is 14.11627 u.

Let’s calculate the mass defect

$Δm = 14Ccal-14CobsCalculated mass of 14C =14.11627 uActual mass of 14C =14.003242 u$

$=14.11627 u -14.003242 u= 0.113028 u$

Mass defect of $14C$ is 0.113028 u.

Let’s find the binding energy

$1 J = 1 kg m2 s-2$

$E = (Δm)c2Δm = mass defect = 0.113028 u= 0.113028 u×( 1 .66054×10 -27 kgu) × (3× 10 8)2=1.68685 × 10-11 kg m2s-2=1.68685 × 10-11 J$

Let’s calculate the energy release when $14C$ nucleus forms from its constituent nucleon. For 1 mole of $14C$ nuclei.

$E =( 1 .68685×10 -11 J 1 atom)( 6 .02214×10 23 atoms 1 mol)= 10.15845×1012 J/mol= 10.15845×109 kJ/mol$

Energy released by 1 mole of $14C$ nuclei is $10.15845 × 109 kJ/mol$ .

If it takes 360kJ of energy to keeps a 100-watt light bulb burning for 1 hour.

Assuming light bulb won’t burn out.

Let’s calculate the how many years this energy of carbon -14 could keep bulb burning.

From the given, 360 kJ will burn for 1 hour.

$(10.15845 × 109 kJ) (1 hr360 kJ) = 2.821791× 107 hrs$

Let’s converts hours into days.

$1 day = 24 hrs1 year = 365 days$

$=(2.821791×107 hrs)( 1 day 24 hrs)( 1 year 365 days)=3221 years$

Therefore, the mass defect energy keeps the burning up to 3221 years.

Conclusion

Therefore, the mass defect energy keeps the burning up to 3221 years.

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Answer 4

Question

Chapter 14, Problem 14.43PAE

Interpretation Introduction

Interpretation: To determine the how many number of years keep burning the bulb by mass defect energy of 1mole $14C$ keep a 100-W light bulb burning.

Concept introduction: Mass defect:

The nucleus of each atom (aside from $11H$ ) has a mass lower than expected from adding the masses of its neutrons and protons.

Mass and energy are related by following equation.

$E=mc2$

E= Energy

m= mass

c = speed of light.

Loss of mass and liberation of energy are related by Einstein’s equations.

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Expert Solution & Answer

Answer to Problem 14.43PAE

Solution:

The mass defect energy keeps the burning up to 3221years.

Explanation of Solution

Formula used:

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Calculation: Let’s calculate the calculated mass of $14C$

$14C$ have six protons and eight neutrons.

$14Ccal= mH+ mNMass of proton =1.007825 uMass of neutron =1.008665 u$

$=6(1.007825 u) + 8(1.008665 u)=6.04695 u + 8.06932 u=14.11627 u$

The calculated mass of $14C$ is 14.11627 u.

Let’s calculate the mass defect

$Δm = 14Ccal-14CobsCalculated mass of 14C =14.11627 uActual mass of 14C =14.003242 u$

$=14.11627 u -14.003242 u= 0.113028 u$

Mass defect of $14C$ is 0.113028 u.

Let’s find the binding energy

$1 J = 1 kg m2 s-2$

$E = (Δm)c2Δm = mass defect = 0.113028 u= 0.113028 u×( 1 .66054×10 -27 kgu) × (3× 10 8)2=1.68685 × 10-11 kg m2s-2=1.68685 × 10-11 J$

Let’s calculate the energy release when $14C$ nucleus forms from its constituent nucleon. For 1 mole of $14C$ nuclei.

$E =( 1 .68685×10 -11 J 1 atom)( 6 .02214×10 23 atoms 1 mol)= 10.15845×1012 J/mol= 10.15845×109 kJ/mol$

Energy released by 1 mole of $14C$ nuclei is $10.15845 × 109 kJ/mol$ .

If it takes 360kJ of energy to keeps a 100-watt light bulb burning for 1 hour.

Assuming light bulb won’t burn out.

Let’s calculate the how many years this energy of carbon -14 could keep bulb burning.

From the given, 360 kJ will burn for 1 hour.

$(10.15845 × 109 kJ) (1 hr360 kJ) = 2.821791× 107 hrs$

Let’s converts hours into days.

$1 day = 24 hrs1 year = 365 days$

$=(2.821791×107 hrs)( 1 day 24 hrs)( 1 year 365 days)=3221 years$

Therefore, the mass defect energy keeps the burning up to 3221 years.

Conclusion

Therefore, the mass defect energy keeps the burning up to 3221 years.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 14, Problem 14.43PAE

Interpretation Introduction

Interpretation: To determine the how many number of years keep burning the bulb by mass defect energy of 1mole $14C$ keep a 100-W light bulb burning.

Concept introduction: Mass defect:

The nucleus of each atom (aside from $11H$ ) has a mass lower than expected from adding the masses of its neutrons and protons.

Mass and energy are related by following equation.

$E=mc2$

E= Energy

m= mass

c = speed of light.

Loss of mass and liberation of energy are related by Einstein’s equations.

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Expert Solution & Answer

Answer to Problem 14.43PAE

Solution:

The mass defect energy keeps the burning up to 3221years.

Explanation of Solution

Formula used:

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Calculation: Let’s calculate the calculated mass of $14C$

$14C$ have six protons and eight neutrons.

$14Ccal= mH+ mNMass of proton =1.007825 uMass of neutron =1.008665 u$

$=6(1.007825 u) + 8(1.008665 u)=6.04695 u + 8.06932 u=14.11627 u$

The calculated mass of $14C$ is 14.11627 u.

Let’s calculate the mass defect

$Δm = 14Ccal-14CobsCalculated mass of 14C =14.11627 uActual mass of 14C =14.003242 u$

$=14.11627 u -14.003242 u= 0.113028 u$

Mass defect of $14C$ is 0.113028 u.

Let’s find the binding energy

$1 J = 1 kg m2 s-2$

$E = (Δm)c2Δm = mass defect = 0.113028 u= 0.113028 u×( 1 .66054×10 -27 kgu) × (3× 10 8)2=1.68685 × 10-11 kg m2s-2=1.68685 × 10-11 J$

Let’s calculate the energy release when $14C$ nucleus forms from its constituent nucleon. For 1 mole of $14C$ nuclei.

$E =( 1 .68685×10 -11 J 1 atom)( 6 .02214×10 23 atoms 1 mol)= 10.15845×1012 J/mol= 10.15845×109 kJ/mol$

Energy released by 1 mole of $14C$ nuclei is $10.15845 × 109 kJ/mol$ .

If it takes 360kJ of energy to keeps a 100-watt light bulb burning for 1 hour.

Assuming light bulb won’t burn out.

Let’s calculate the how many years this energy of carbon -14 could keep bulb burning.

From the given, 360 kJ will burn for 1 hour.

$(10.15845 × 109 kJ) (1 hr360 kJ) = 2.821791× 107 hrs$

Let’s converts hours into days.

$1 day = 24 hrs1 year = 365 days$

$=(2.821791×107 hrs)( 1 day 24 hrs)( 1 year 365 days)=3221 years$

Therefore, the mass defect energy keeps the burning up to 3221 years.

Conclusion

Therefore, the mass defect energy keeps the burning up to 3221 years.

Answer 6

Chapter 14, Problem 14.43PAE

Interpretation Introduction

Interpretation: To determine the how many number of years keep burning the bulb by mass defect energy of 1mole $14C$ keep a 100-W light bulb burning.

Concept introduction: Mass defect:

The nucleus of each atom (aside from $11H$ ) has a mass lower than expected from adding the masses of its neutrons and protons.

Mass and energy are related by following equation.

$E=mc2$

E= Energy

m= mass

c = speed of light.

Loss of mass and liberation of energy are related by Einstein’s equations.

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Expert Solution & Answer

Answer to Problem 14.43PAE

Solution:

The mass defect energy keeps the burning up to 3221years.

Explanation of Solution

Formula used:

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Calculation: Let’s calculate the calculated mass of $14C$

$14C$ have six protons and eight neutrons.

$14Ccal= mH+ mNMass of proton =1.007825 uMass of neutron =1.008665 u$

$=6(1.007825 u) + 8(1.008665 u)=6.04695 u + 8.06932 u=14.11627 u$

The calculated mass of $14C$ is 14.11627 u.

Let’s calculate the mass defect

$Δm = 14Ccal-14CobsCalculated mass of 14C =14.11627 uActual mass of 14C =14.003242 u$

$=14.11627 u -14.003242 u= 0.113028 u$

Mass defect of $14C$ is 0.113028 u.

Let’s find the binding energy

$1 J = 1 kg m2 s-2$

$E = (Δm)c2Δm = mass defect = 0.113028 u= 0.113028 u×( 1 .66054×10 -27 kgu) × (3× 10 8)2=1.68685 × 10-11 kg m2s-2=1.68685 × 10-11 J$

Let’s calculate the energy release when $14C$ nucleus forms from its constituent nucleon. For 1 mole of $14C$ nuclei.

$E =( 1 .68685×10 -11 J 1 atom)( 6 .02214×10 23 atoms 1 mol)= 10.15845×1012 J/mol= 10.15845×109 kJ/mol$

Energy released by 1 mole of $14C$ nuclei is $10.15845 × 109 kJ/mol$ .

If it takes 360kJ of energy to keeps a 100-watt light bulb burning for 1 hour.

Assuming light bulb won’t burn out.

Let’s calculate the how many years this energy of carbon -14 could keep bulb burning.

From the given, 360 kJ will burn for 1 hour.

$(10.15845 × 109 kJ) (1 hr360 kJ) = 2.821791× 107 hrs$

Let’s converts hours into days.

$1 day = 24 hrs1 year = 365 days$

$=(2.821791×107 hrs)( 1 day 24 hrs)( 1 year 365 days)=3221 years$

Therefore, the mass defect energy keeps the burning up to 3221 years.

Conclusion

Therefore, the mass defect energy keeps the burning up to 3221 years.

Answer 7

Chapter 14, Problem 14.43PAE

Interpretation Introduction

Interpretation: To determine the how many number of years keep burning the bulb by mass defect energy of 1mole $14C$ keep a 100-W light bulb burning.

Concept introduction: Mass defect:

The nucleus of each atom (aside from $11H$ ) has a mass lower than expected from adding the masses of its neutrons and protons.

Mass and energy are related by following equation.

$E=mc2$

E= Energy

m= mass

c = speed of light.

Loss of mass and liberation of energy are related by Einstein’s equations.

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Answer 8

Expert Solution & Answer

Answer to Problem 14.43PAE

Solution:

The mass defect energy keeps the burning up to 3221years.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Formula used:

$E = (Δm)c2Δm = Mass defectc = Velocity of light$

Calculation: Let’s calculate the calculated mass of $14C$

$14C$ have six protons and eight neutrons.

$14Ccal= mH+ mNMass of proton =1.007825 uMass of neutron =1.008665 u$

$=6(1.007825 u) + 8(1.008665 u)=6.04695 u + 8.06932 u=14.11627 u$

The calculated mass of $14C$ is 14.11627 u.

Let’s calculate the mass defect

$Δm = 14Ccal-14CobsCalculated mass of 14C =14.11627 uActual mass of 14C =14.003242 u$

$=14.11627 u -14.003242 u= 0.113028 u$

Mass defect of $14C$ is 0.113028 u.

Let’s find the binding energy

$1 J = 1 kg m2 s-2$

$E = (Δm)c2Δm = mass defect = 0.113028 u= 0.113028 u×( 1 .66054×10 -27 kgu) × (3× 10 8)2=1.68685 × 10-11 kg m2s-2=1.68685 × 10-11 J$

Let’s calculate the energy release when $14C$ nucleus forms from its constituent nucleon. For 1 mole of $14C$ nuclei.

$E =( 1 .68685×10 -11 J 1 atom)( 6 .02214×10 23 atoms 1 mol)= 10.15845×1012 J/mol= 10.15845×109 kJ/mol$

Energy released by 1 mole of $14C$ nuclei is $10.15845 × 109 kJ/mol$ .

If it takes 360kJ of energy to keeps a 100-watt light bulb burning for 1 hour.

Assuming light bulb won’t burn out.

Let’s calculate the how many years this energy of carbon -14 could keep bulb burning.

From the given, 360 kJ will burn for 1 hour.

$(10.15845 × 109 kJ) (1 hr360 kJ) = 2.821791× 107 hrs$

Let’s converts hours into days.

$1 day = 24 hrs1 year = 365 days$

$=(2.821791×107 hrs)( 1 day 24 hrs)( 1 year 365 days)=3221 years$

Therefore, the mass defect energy keeps the burning up to 3221 years.

Answer 12

Conclusion

Therefore, the mass defect energy keeps the burning up to 3221 years.

Answer 13

Ch. 14 - Prob. 1CO Ch. 14 - Prob. 2CO Ch. 14 - Prob. 3CO Ch. 14 - Prob. 4CO Ch. 14 - Prob. 5CO Ch. 14 - Prob. 6CO Ch. 14 - Prob. 7CO Ch. 14 - Prob. 8CO Ch. 14 - Prob. 9CO Ch. 14 - Prob. 10CO

Concept explainers

Answer to Problem 14.43PAE

Explanation of Solution

Want to see more full solutions like this?

Chapter 14 Solutions